Systems and methods for high dynamic range image reconstruction

ABSTRACT

Systems and method for expanding a dynamic range associated with an image are disclosed. The method includes capturing an image of a scene via an imaging device using a single exposure. The image of the scene includes a plurality of polarization images corresponding to different angles of polarization, and each of the polarization images comprise a plurality of color channels. The method further includes determining a criterion for each of the plurality of color channels; selecting one color channel of the plurality of color channels based on determining of the criterion; generating a reconstructed image irradiance for the one color channel based on pixels in two or more of the plurality of polarization images obtained for the one color channel; and outputting a reconstructed image with the reconstructed image irradiance.

FIELD

Aspects of embodiments of the present disclosure relate to the field of digital image processing, and more particularly, to reconstructing the image irradiance of an image using a single exposure.

BACKGROUND

Robotics and other types of computer vision applications may benefit from increased dynamic range of images than what is provided by current imaging devices. Current imaging devices may have limited dynamic range that may result in loss of detail in bright or dark areas.

The above information disclosed in this Background section is only for enhancement of understanding of the background of the present disclosure, and therefore, it may contain information that does not form prior art.

SUMMARY

An embodiment of the present disclosure is directed to a method for expanding a dynamic range associated with an image. The method includes capturing an image of a scene via an imaging device using a single exposure. The image of the scene includes a plurality of polarization images corresponding to different angles of polarization, and each of the polarization images comprise a plurality of color channels. The method further includes determining a criterion for each of the plurality of color channels; selecting one color channel of the plurality of color channels based on determining of the criterion; generating a reconstructed image irradiance for the one color channel based on pixels in two or more of the plurality of polarization images obtained for the one color channel; and outputting a reconstructed image with the reconstructed image irradiance.

According to one embodiment, the reconstructed image irradiance in the one color channel has a higher dynamic range than irradiance supported by the imaging device.

According to one embodiment, the reconstructed image irradiance is based on a spectral irradiance associated with the one color channel.

According to one embodiment, the generating the reconstructed image irradiance for the one color channel includes: obtaining an inverse camera response function for the one color channel for mapping pixel values of the pixels to corresponding polarized irradiance values; and combining the polarized irradiance values.

According to one embodiment, the combining of the polarized irradiance values includes applying a weight to the polarized irradiance values.

According to one embodiment, the two of the polarization images are images captured at polarization angles that are 90 degrees apart.

According to one embodiment, the criterion is determining that the one color channel includes a most number of particular pixels, wherein each of the particular pixels are associated with pixel values in at least two of the plurality of polarization images, where the pixel values are above a first threshold or under a second threshold.

According to one embodiment, the generating the reconstructed image irradiance includes: identifying, for a particular pixel, a pixel value above a first threshold or under a second threshold; and in response to identifying the pixel value, estimating a degree of linear polarization (DOLP) and angle of linear polarization (AOLP) for the pixel based on a prior probability distribution of the DOLP and AOLP.

According to one embodiment, the prior probability distribution includes a DOLP and AOLP of one or more neighbor pixels to the particular pixel.

According to one embodiment, the prior probability distribution is formed based on known geometry of an object associated with the particular pixel.

An embodiment of the present disclosure is further directed to a method for expanding a dynamic range associated with an image. The method includes capturing an image of a scene via an imaging device using a single exposure. The image of the scene includes a plurality of polarization images corresponding to different angles of polarization. The method further includes identifying a pixel in one of the plurality of polarization images having a pixel value above a first threshold or under a second threshold; in response to identifying the pixel value, estimating a degree of linear polarization (DOLP) and angle of linear polarization (AOLP) for the pixel based on a prior probability distribution on the DOLP and AOLP; estimating a camera exposure time for each of the plurality of polarization angles based on the estimated DOLP and AOLP; generating a reconstructed image irradiance for the image based on pixel values in the plurality of polarization images and corresponding camera exposure times; and outputting a reconstructed image with the reconstructed image irradiance.

According to one embodiment, the reconstructed image irradiance has a higher dynamic range than irradiance supported by the imaging device.

According to one embodiment, the generating the reconstructed image irradiance includes: obtaining an inverse camera response function for mapping the pixel values to corresponding polarized irradiance values; and combining the polarized irradiance values.

According to one embodiment, the combining of the polarized irradiance values includes applying a weight to the polarized irradiance values.

According to one embodiment, the prior probability distribution includes a DOLP and AOLP of one or more neighbor pixels to the pixel.

According to one embodiment, the prior probability distribution is formed based on known geometry of an object associated with the pixel.

An embodiment of the present disclosure is also directed to a method for expanding a dynamic range associated with an image. The method comprises: capturing an image of a scene via an imaging device using a single exposure, the image of the scene comprising a plurality of polarization images corresponding to different angles of polarization, each of the polarization images comprising a plurality of color channels; generating a plurality of polarization image features based on the plurality of polarization images; and supplying the polarization image features to a convolutional neural network trained to generate a reconstructed image having an expanded dynamic range.

According to one embodiment, the generating the polarization image features comprises computing a degree of linear polarization (DOLP) and an angle of linear polarization (AOLP) based on the polarization images.

According to one embodiment, the convolutional neural network comprises a neural decoder.

According to one embodiment, the convolutional neural network comprises an encoder-decoder network.

According to one embodiment, the convolutional neural network is trained based on training data, wherein the training data includes a training set of polarization images corresponding to different angles of polarization and corresponding training set of high dynamic range images.

According to one embodiment, the training set of high dynamic range images are captured using multiple exposures at different exposure settings.

According to one embodiment, the training set of polarization images and the corresponding training set of high dynamic range images are synthesized.

An embodiment of the present disclosure is also directed to an imaging system comprising a polarization camera comprising: a polarizing filter configured to capture a plurality of polarization images using a single exposure, the plurality of polarization images corresponding to different angles of polarization, each of the polarization images comprising a plurality of color channels; and a processing system coupled to the polarization camera. The processing system comprises a processor and memory storing instructions that, when executed by the processor, cause the processor to perform: determining a criterion for each of the plurality of color channels; selecting one color channel of the plurality of color channels based on determining of the criterion; generating a reconstructed image irradiance for the one color channel based on pixels in two or more of the plurality of polarization images obtained for the one color channel; and outputting a reconstructed image with the reconstructed image irradiance.

An embodiment of the present disclosure is further directed to an imaging system comprising: a polarization camera comprising a polarizing filter configured to capture a plurality of polarization images using a single exposure, the plurality of polarization images corresponding to different angles of polarization; and a processing system coupled to the polarization camera. The processing system comprising a processor and memory storing instructions that, when executed by the processor, cause the processor to perform: identifying, a pixel in one of the plurality of polarization images having a pixel value above a first threshold or under a second threshold; in response to identifying the pixel value, estimating a degree of linear polarization (DOLP) and angle of linear polarization (AOLP) for the pixel based on a prior probability distribution on the DOLP and AOLP; estimating a camera exposure time for each of the plurality of polarization angles based on the estimated DOLP and AOLP; generating a reconstructed image irradiance for the image based on pixel values in the plurality of polarization images and corresponding camera exposure times; and outputting a reconstructed image with the reconstructed image irradiance.

These and other features, aspects and advantages of the embodiments of the present disclosure will be more fully understood when considered with respect to the following detailed description, appended claims, and accompanying drawings. Of course, the actual scope of the invention is defined by the appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

Non-limiting and non-exhaustive embodiments of the present embodiments are described with reference to the following figures, wherein like reference numerals refer to like parts throughout the various views unless otherwise specified.

FIG. 1A is a block diagram of a system for generating high dynamic range (HDR) images according to one embodiment;

FIG. 1B is a perspective view of a polarization camera module according to one embodiment of the present disclosure;

FIG. 1C is a cross sectional view of a portion of a polarization camera module according to one embodiment of the present disclosure;

FIG. 2 is a conceptual layout diagram of a process for converting scene radiance into pixel values for a polarization camera according to one embodiment;

FIG. 3A is a flow diagram of a process executed by a processing circuit for HDR image reconstruction according to one embodiment;

FIG. 3B is a more detailed flow diagram for reconstructing the image irradiance of pixels in an image in a selected color channel according to one embodiment;

FIG. 4 is a conceptual layout diagram of images pixels and corresponding pixel values across different polarization images and color channels according to one embodiment; and

FIG. 5 is a flow diagram of a process executed by the processing circuit for HDR image reconstruction according to one embodiment.

DETAILED DESCRIPTION

Hereinafter, example embodiments will be described in more detail with reference to the accompanying drawings, in which like reference numbers refer to like elements throughout. The present disclosure, however, may be embodied in various different forms, and should not be construed as being limited to only the illustrated embodiments herein. Rather, these embodiments are provided as examples so that this disclosure will be thorough and complete, and will fully convey the aspects and features of the present disclosure to those skilled in the art. Accordingly, processes, elements, and techniques that are not necessary to those having ordinary skill in the art for a complete understanding of the aspects and features of the present disclosure may not be described. Unless otherwise noted, like reference numerals denote like elements throughout the attached drawings and the written description, and thus, descriptions thereof may not be repeated. Further, in the drawings, the relative sizes of elements, layers, and regions may be exaggerated and/or simplified for clarity.

The dynamic range of an imaging device may be defined as a ratio between the brightest and darkest image irradiance that the device is capable of measuring. In general terms, the dynamic range of human vision is on the order of 4,000 times greater than the dynamic range of a conventional imaging device. Due to the limited dynamic range, images taken by the imaging device of high-contrast scenes may contain regions with over-exposed or under-exposed pixels, and fail to convey the true image irradiance in these regions.

Current art mechanisms exist for increasing the dynamic range of an image. Such mechanisms may include capturing multiple images at different exposures, and merging the multiple exposures to generate a higher dynamic range image. Such current art mechanism, however, is deficient in that such technique can generally be only used with static scenes as the images may depict motion blur for any objects that move in the scene. In addition, capturing multiple exposures using different aperture settings can also cause the appearance of different depths of field, resulting in some parts of the scene showing different levels of focus blur between different exposures. Yet another deficiency may be that capturing multiple exposures with different gain settings may cause differences in sensor noise levels between the different exposures.

Although an existing art mechanism proposes increasing the dynamic range of an image using different polarization images that avoids the need to capture multiple images at different exposures, a drawback to such existing art mechanism is that some of the polarization images may include over/underexposed pixels that corrupt the estimating of a degree and angle of polarization of the pixels, which are used to estimate camera exposure times, which in turn are used in current art HDR image reconstruction algorithms.

Accordingly, it is desirable to expand the dynamic range of an image captured by an imaging device, using a single exposure.

In general terms, embodiments of the present disclosure are directed to high dynamic range (HDR) image reconstruction using polarization imaging. In one embodiment, HDR image reconstruction includes reconstructing irradiance of an image so that the dynamic range of the reconstructed irradiance is greater than the dynamic range possible/supported by an underlying sensor of the imaging device. In this regard, a polarization camera may be used to capture an image of a scene with the polarizing filter set at various polarization angles. Depending on the angle of the polarizing filter, irradiance attenuations may be obtained. In this regard, the different angles of the polarizing filter may function similarly to changing the exposure setting (e.g. changing the exposure time settings) of an imaging device, and generate multiple polarization images with different irradiance measurements. The irradiance derived from the pixel values in the multiple polarization images may then be combined to generate a reconstructed image irradiance. HDR images may provide more detail in regions of images that would be overexposed or underexposed when captured by a conventional imaging system, thereby improving the performance of computer vision or machine vision systems, such as by performing more accurate image classification.

One problem that may arise in trying to reconstruct the image irradiance from the multiple polarization angles is that some pixels in some of the polarization images may be over or underexposed, resulting in a corrupted measurement of the angle and degree of polarization which may be needed to reconstruct the image irradiance for that pixel. According to one embodiment, one solution to this problem entails processing the color polarization images for identifying the polarized irradiance at each polarization angle on a per-color channel basis (e.g. separately for red (R), green (G), and blue (B) color channels). An over/underexposed pixel in one color channel may not be over/underexposed in another color channel.

In one embodiment, the polarized irradiance of each pixel at each color channel is examined for identifying the color channel with a least number of over/underexposed pixels in a polar sense. In one embodiment, an over/underexposed pixel in the polar sense is a pixel which, out of the various polarization angle measurements, the pixel value in two or more of the polarization angle measurements for the pixel is under or overexposed. Once the color channel with the least number of over/underexposed pixels in the polar sense is identified, image irradiance reconstruction may be performed on only the identified color channel, helping minimize the negative effects of over/underexposed pixels.

As discussed, a problem presented by over/underexposed pixels is that they may prevent accurate estimation of the angle and degree of polarization for the pixels that can be used to compute corresponding equivalent camera exposure times. This may prevent usage of current art HDR image reconstruction algorithms that rely on determining exposure times for image irradiance reconstruction. One such current art reconstruction algorithm is described in P. E. Debevec and J. Malik, “Recovering High Dynamic Range Radiance Maps from Photographs,” in ACM SIGGRAPH 2008 classes, pp. 1-10, the content of which is incorporated herein by reference. In one embodiment, the problem is addressed by estimating the polarization degree and angle of an over/underexposed pixel from a prior probability distribution of degrees and angles of linear polarization that are known or partially known (e.g., a Bayesian prior in accordance with a Bayesian model of the distribution of DOLP and AOLP). In one example, the prior distribution may be based on smoothness assumptions where the polarization degree and angle are estimated from a neighborhood of pixels that are not over/underexposed. In another example, the polarization degree and angle of an over/underexposed pixel may be estimated based on the geometry of an object through Fresnel equations. Once the degree and angle of polarization for the over/underexposed pixel are known, and if there is at least one value in one polarization angle where the pixel is not over/underexposed, the pixel value may be used for image irradiance reconstruction.

FIG. 1A is a block diagram of a system for generating high dynamic range (HDR) images according to one embodiment. Hereinafter, a reconstructed image that has a dynamic range higher than the dynamic range supported by an imaging device is referred to as an HDR image. In the arrangement shown in FIG. 1A, a scene 1 includes various types of objects 2. A polarization camera 10 has a lens 12 with a field of view, where the lens 12 and the camera 10 are oriented such that the field of view encompasses the scene 1. The lens 12 is configured to direct light (e.g., focus light) from the scene 1 onto a light sensitive medium such as an image sensor 14 (e.g., a complementary metal oxide semiconductor (CMOS) image sensor or charge-coupled device (CCD) image sensor).

The polarization camera 10 further includes a polarizer or polarizing filter or polarization mask 16 placed in the optical path between the scene 1 and the image sensor 14. According to various embodiments of the present disclosure, the polarizer or polarization mask 16 is configured to enable the polarization camera 10 to capture images of the scene 1 with the polarizer set at various specified angles (e.g., at 45° rotations or at 60° rotations or at non-uniformly spaced rotations).

As one example, FIG. 1A depicts an embodiment where the polarization mask 16 is a polarization mosaic aligned with the pixel grid of the image sensor 14 in a manner similar to a red-green-blue (RGB) color filter (e.g., a Bayer filter) of a color camera. In a manner similar to how a color filter mosaic filters incoming light based on wavelength such that each pixel in the image sensor 14 receives light in a particular portion of the spectrum (e.g., red, green, or blue) in accordance with the pattern of color filters of the mosaic, a polarization mask 16 using a polarization mosaic filters light based on linear polarization such that different pixels receive light at different angles of linear polarization (e.g., at 0°, 45°, 90°, and 135°, or at 0°, 60° degrees, and 120°. Accordingly, the polarization camera 10 using a polarization mask 16 such as that shown in FIG. 1A is capable of concurrently or simultaneously capturing light at four different linear polarizations. One example of a polarization camera is the Blackfly® S Polarization Camera produced by FLIR® Systems, Inc. of Wilsonville, Oreg.

While the above description relates to some possible implementations of a polarization camera using a polarization mosaic, embodiments of the present disclosure are not limited thereto and encompass other types of polarization cameras that are capable of capturing images at multiple different polarizations. For example, the polarization filter 16 may have fewer than or more than four different polarizations, or may have polarizations at different angles (e.g., at angles of polarization of: 0°, 60° degrees, and 120° or at angles of polarization of 0°, 30°, 60°, 90°, 120°, and 150°. As another example, the polarization filter 16 may be implemented using an electronically controlled polarization filter, such as an electro-optic modulator (e.g., may include a liquid crystal layer), where the polarization angles of the individual pixels of the filter may be independently controlled, such that different portions of the image sensor 14 receive light having different polarizations. Furthermore, while the above examples relate to the use of a linear polarizing filter, embodiments of the present disclosure are not limited thereto and also include the use of polarization cameras that include circular polarizing filters (e.g., linear polarizing filters with a quarter wave plate). Accordingly, in some embodiments of the present disclosure, a polarization camera uses a polarizing filter to capture multiple polarization raw frames at different polarizations of light, such as different linear polarization angles and different circular polarizations (e.g., handedness).

FIG. 1B is a perspective view of a polarization camera module according to one embodiment of the present disclosure. FIG. 1C is a cross sectional view of a portion of a polarization camera module according to one embodiment of the present disclosure. Some aspects of embodiments of the present disclosure relate to a polarization camera module in which multiple polarization cameras (e.g., multiple cameras, where each camera has a polarizing filter in its optical path) are arranged adjacent to one another and in an array and may be controlled to capture images in a group (e.g., a single trigger may be used to control all of the cameras in the system to capture images concurrently or substantially simultaneously). The polarizing filters in the optical paths of each of the cameras in the array cause differently polarized light to reach the image sensors of the cameras. The individual polarization cameras in the camera system have optical axes that are substantially perpendicular to one another, are placed adjacent to one another, and have substantially the same field of view, such that the cameras in the camera system capture substantially the same view of a scene 1, but with different polarizations. In some embodiments, the individual polarization cameras are arranged such that parallax shift between cameras is substantially negligible based on the designed operating distance of the camera system to objects in the scene, where larger spacings between the cameras may be tolerated if the designed operating distance is large.

For example, in the embodiment of the polarization camera module 10′ shown in FIG. 1B, four cameras 10A′, 10B′, 10C′, and 10D′ are arranged in a 2×2 grid to form a camera array, where the four cameras have substantially parallel optical axes. The four cameras may be controlled together such that they capture images substantially simultaneously and using the same exposure settings (e.g., same aperture, length of exposure, and gain or “ISO” settings). In various embodiments of the present disclosure, each of the separate cameras 10A′, 10B′, 10C′, and 10D′ includes a different polarizing filter.

FIG. 1C shows a cross sectional view of two of the polarization cameras 10A′ and 10B′ shown in FIG. 1B. As seen in FIG. 1C, each a polarization camera (10A′ and 10B′) system includes a corresponding lens, a corresponding image sensor, and a corresponding polarizing filter. In particular, polarization camera 10A′ includes lens 12A′, image sensor 14A′, and polarizing filter 16A′. Likewise, polarization camera 10B′ includes lens 12B′, image sensor 14B′, and polarizing filter 16B′. In some embodiments of the present disclosure, the image sensors four cameras 10A′, 10B′, 10C′, and 10D′ are monolithically formed on a same semiconductor die, and the four cameras are located in a same housing with separate apertures for the lenses 12 corresponding to the different image sensors. Similarly, the polarizing filters 16 may correspond to different portions of a single physical layer that has different polarizing filters (e.g., different linear polarizing angles) in different regions of the layer (corresponding to the different cameras).

In some embodiments of the present disclosure, each of the cameras in the camera system 10′ has a corresponding polarizing filter that is configured to filter differently polarized light. For example, in the embodiment shown in FIG. 1C, polarizing filter 16A′ of camera 10A′ may be a linear polarizing filter oriented at an angle of 0°, polarizing filter 16B′ of camera 10B′ may be a linear polarizing filter oriented at an angle of 45°, polarizing filter 16C′ of camera 10C′ may be a linear polarizing filter oriented at an angle of 90°, and polarizing filter 16D′ of camera 10D′ may be a linear polarizing filter oriented at an angle of 135°. In some embodiments, one or more of the cameras may include a circular polarizer. In some embodiments of the present disclosure, the camera system 10′ includes polarizing filters configured to filter light in at least two different polarizations. In some embodiments of the present disclosure, the camera system 10′ includes polarizing filters configured to filter light in at least three different polarizations. In the embodiment shown in FIG. 1C, the polarizing filter 16 is located behind the lens 12 (e.g., between the lens 12 and the image sensor 14), but embodiments of the present disclosure are not limited thereto. In some embodiments, the polarizing filter is located in front of the lens 12.

In some embodiments, the various individual cameras of the camera array are registered with one another by determining their relative poses (or relative positions and orientations) by capturing multiple images of a calibration target, such as a checkerboard pattern, an ArUco target (see, e.g., Garrido-Jurado, Sergio, et al. “Automatic generation and detection of highly reliable fiducial markers under occlusion.” Pattern Recognition 47.6 (2014): 2280-2292.) or a ChArUco target (see, e.g., An, Gwon Hwan, et al. “Charuco board-based omnidirectional camera calibration method.” Electronics 7.12 (2018): 421.). In particular, the process of calibrating the targets may include computing intrinsic matrices characterizing the internal parameters of each camera (e.g., matrices characterizing the focal length, image sensor format, and principal point of the camera) and extrinsic matrices characterizing the pose of each camera with respect to world coordinates (e.g., matrices for performing transformations between camera coordinate space and world or scene coordinate space).

While not shown in FIG. 1C, in some embodiments of the present disclosure, each polarization camera may also include a color filter having in a mosaic pattern such as a Bayer filter, such that individual pixels of the image sensors 14 receive light corresponding to, for example, red (R), green (G), and blue (B) portions of the spectrum, such that each camera captures light in a visible portion of the electromagnetic spectrum in accordance with a mosaic pattern. In some embodiments, a demosaicing process is used to compute separate red, green, and blue channels from the raw data. In some embodiments of the present disclosure, each polarization camera may be used without a color filter or with filters used to transmit or selectively transmit various other portions of the electromagnetic spectrum, such as infrared light.

As a result, the polarization camera captures multiple input images (or polarization raw frames) of the scene 1, where each of the polarization raw frames corresponds to an image taken behind a polarization filter at a different angle of polarization ϕ_(pol) (e.g., 0 degrees, 45 degrees, 90 degrees, or 135 degrees). In one embodiment, each of the polarization raw frames is captured from substantially the same pose with respect to the scene 1 (e.g., the images captured with the polarization filter at 0 degrees, 45 degrees, 90 degrees, or 135 degrees are all captured by a same polarization camera located at a same location and orientation), as opposed to capturing the polarization raw frames from disparate locations and orientations with respect to the scene. Thus, according to one embodiment, a particular point of an image (referred to as an image pixel), is depicted by corresponding pixels in the polarization raw frames, for a total of four pixel values (also referred to as a quad block of pixels) associated with the image pixel. The polarization camera 10 may be configured to detect light in a variety of different portions of the electromagnetic spectrum, such as the human-visible portion of the electromagnetic spectrum, red, green, and blue portions of the human-visible spectrum, as well as invisible portions of the electromagnetic spectrum such as infrared and ultraviolet.

Referring again to the system of FIG. 1A, in one embodiment, after passing through the polarization filter 16, the irradiance of the scene 1, referred to as the scene irradiance I₀, changes according to the following equation:

I _(i)=½I ₀(1+ρ cos(2(Θ−α_(i))))  (1)

where I_(i) is an irradiance after passing through the polarizing filter 16 with an angle α_(i), ρ is a degree of polarization, and Θ is an angle of polarization. Equation (1) is described in more detail in X. Wu et al, “HDR Reconstruction Based on the Polarization Camera,” IEEE Robotics and Automation Letters (RAL) paper presented at the 2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Oct. 25-29, 2020, Las Vegas, Nev., the content of which is incorporated herein by reference.

In one embodiment, the angles of polarizing filters are set 45 degrees apart from each other (e.g., set to 0, 45, 90 and 135 degrees), for respectively capturing polarized irradiances I₁, I₂, I₃, I₄. In this case, Equation (1) may be simplified as follows:

I ₁=½I ₀(1+ρ cos(2Θ))

I ₂=½I ₀(1+ρ sin(2Θ))

I ₃=½I ₀(1−ρ cos(2Θ))

I ₄=½I ₀(1−ρ sin(2Θ))

In one embodiment, the polarization camera 10 further includes a color filter 17 having a mosaic pattern such as, for example, a Bayer filter. The color filter 17 may allow individual pixels of the image sensors 14 receive light corresponding to, for example, red (R), green (G), and blue (B) portions of the spectrum, such that each camera captures light in a visible portion of the electromagnetic spectrum in accordance with a mosaic pattern. In some embodiments, a demosaicing process is used to compute separate red, green, and blue channels from the raw polarization data.

In one embodiment, after passing through the color filter 17, the polarized irradiances I₁, I₂, I₃, I₄ change according to spectral response function s_(C) for the particular color channel:

$I_{iC} = {{s_{C}\left( I_{i} \right)} = {\int\limits_{\lambda}{{S_{C}(\lambda)}{E_{i}(\lambda)}d{\lambda.}}}}$

where C is a color channel index (e.g. red, green, or blue), λ is wavelength of light, and E is spectral irradiance or density. In general terms, the spectral response function may represent how much light is passed through the color filter for the light received at wavelength λ. A separate spectral response function may be used for each color channel.

In one embodiment, the image sensor 14 receives the light that has passed via the polarization and color filters 16, 17, and generates color polarization raw frames 18 (also referred to as polarization digital images) L_(i,C), for each polarization angle and each color channel, using a camera response function f_(C) as follows:

L_(i, C) = f_(C)(I_(ic)t₀)or $\begin{matrix} {L_{i,C} = {f_{C}\left( {{s_{C}\left( {I_{0}\frac{1}{2}\left( {1 + {\rho{\cos\left( {2\left( {\Theta - \alpha_{i}} \right)} \right)}}} \right)} \right)}t_{0}} \right)}} \\ {= {f_{C}\left( {\int\limits_{\lambda}{{S_{C}(\lambda)}{E_{0}(\lambda)}\frac{1}{2}\left( {1 + {\rho{\cos\left( {2\left( {\Theta - \alpha_{i}} \right)} \right)}}} \right)d\lambda t_{0}}} \right)}} \\ {= {f_{C}\left( {s_{C}\left( {t_{0}I_{0}\frac{1}{2}\left( {1 + {\rho\cos\left( {2\left( {\Theta - \alpha_{i}} \right)} \right)}} \right)} \right)} \right)}} \\ {= {f_{C}\left( {s_{C}\left( {I_{0}t_{i}} \right)} \right)}} \end{matrix}$

where t₀ is a camera exposure time of a single exposure, which may be set as desired to affect the polarization images.

Rather than identifying f_(C), an inverse camera response function g may be estimated given that the camera response function is a monotonic function, as discussed in further detail the above-referenced paper by X. Wu et al, “HDR Reconstruction Based on the Polarization Camera,” as follows:

It=g(L)

Therefore:

s _(C)(I ₀ t _(i))=g _(C)(L _(i,C))

When each polarized digital image in a particular color channel L_(1,C), L_(2,C), L_(3,C), and L_(4,C) is considered separately:

${{g_{C}\left( L_{1,C} \right)} = {s_{C}\left( {t_{0}I_{0}\frac{1}{2}\left( {1 + {\rho{\cos\left( {2\Theta} \right)}}} \right)} \right)}},$ ${{g_{C}\left( L_{2,C} \right)} = {s_{C}\left( {t_{0}I_{0}\frac{1}{2}\left( {1 + {\rho{\sin\left( {2\Theta} \right)}}} \right)} \right)}},$ ${{g_{C}\left( L_{3,C} \right)} = {s_{C}\left( {t_{0}I_{0}\frac{1}{2}\left( {1 - {\rho{\cos\left( {2\Theta} \right)}}} \right)} \right)}},$ ${{g_{C}\left( L_{4,C} \right)} = {s_{C}\left( {t_{0}I_{0}\frac{1}{2}\left( {1 - {\rho{\sin\left( {2\Theta} \right)}}} \right)} \right)}},$ $\begin{matrix} {{{g_{C}\left( L_{1,C} \right)} + {g_{C}\left( L_{3,C} \right)}} = {{s_{C}\left( {t_{0}{I_{0}\left( {1 + {\rho{\cos\left( {2\Theta} \right)}}} \right)}} \right)} +}} \\ {s_{C}\left( {t_{0}I_{0}\frac{1}{2}\left( {1 - {\rho{\cos\left( {2\Theta} \right)}}} \right)} \right)} \\ {= {s_{C}\left( {t_{0}I_{0}} \right)}} \\ {= {{s_{C}\left( I_{0} \right)}t_{0}}} \end{matrix}$

And similarly:

g _(C)(L _(2,C))+g _(C)(L _(4,C))=s _(C)(I ₀)t ₀

In one embodiment, the system of FIG. 1A further includes a processing circuit 100 configured to engage in HDR image reconstruction in a particular color channel. In this regard, the processing circuit 100 is configured to estimate an image irradiance s_(C)(I₀) for each image pixel in the particular color channel, based on the pixel irradiance estimates of two or more of the quad block pixels in the corresponding polarization digital images L₁, L₂, L₃, or L₄ for the particular color channel.

Two separate estimations of s_(C)(I₀) may be performed using two of the color polarization digital images that have a 90 degree difference in their polarization angles:

s _(C)(I ₀)=½(g _(C)(L _(1,C))+g _(C)(L _(3,C))),

s _(C)(I ₀)=½(g _(C)(L _(2,C))+g _(C)(L_(4,C)))

In one embodiment, in efforts to increase the dynamic range of the reconstructed image irradiance as much as possible, image irradiance estimates are performed in a color channel with a fewest number of pixels that are over/underexposed that may corrupt the reconstructed irradiance values for the over/underexposed pixels. In this regard, according to one embodiment, the processing circuit 100 is configured to identify, for each of the color channels, all pixels that are over/underexposed in the polar sense. In one embodiment, the processing circuit 100 is configured to select the color channel that has a fewest over/underexposed pixels in the polar sense, helping minimize the negative effects of such pixels. The processing circuit 100 may then perform image irradiance reconstruction for each image pixel of the selected color channel, based on corresponding pixel values in two or more of the polarization images in the selected color channel. In one embodiment, an HDR image 20 may be generated based on the reconstructed image irradiance values of each image pixel. In one embodiment, the non-selected color channels are ignored for purposes of image irradiance reconstruction. Thus, according to one embodiment, the output reconstructed image irradiance is only in the selected color channel.

In one embodiment, the two separate estimations of s_(C)(I₀) in the selected color channel may be combined using a weighted approach. The type of weighted approach for performing image irradiance reconstruction for a particular pixel may depend on the extent of over/underexposure of corresponding pixels across the polarization images. For example, if there is no over/underexposure of the pixel across the polarization angles for the particular pixel, s_(C)(I₀) may be calculated as a weighted sum as follows:

${s_{C}\left( I_{0} \right)} = \left( {{\overset{2}{\sum\limits_{j = 1}}{{w\left( {L_{i,C} + L_{{i + 2},C}} \right)}{\left( {{g_{C}\left( L_{i,C} \right)} + {g_{C}\left( L_{{i + 2},C} \right)}} \right)/\left( {t_{0}{\sum\limits_{i = 1}^{2}{w\left( {L_{i,C} + L_{{i + 2},C}} \right)}}} \right)}}},} \right.$

where w depends on how well the pixels are exposed, and may be implemented with a Gaussian function:

w(L)˜exp(−(L−0.5)²/2σ²)

where σ is a standard deviation that may be predefined. For example, σ=0.2 may be used as a default.

In one embodiment, a problem presented by over/underexposed pixels in a quad block is that those pixels may be needed for estimating a degree of linear polarization ρ (DOLP) an angle of linear polarization Θ (AOLP) for the pixels. Thus, for example, when only two pixels in the quad block taken in two polarization measurements provide accurate values, it may not be feasible to obtain the DOLP and AOLP associated with the pixels. DOLP and AOLP, however, may be needed to estimate an exposure for the pixels (represented as a camera exposure time for the pixels), where the camera exposure times are in turn used in current art HDR image reconstruction algorithms to combine the irradiance estimates from the multiple digital images.

In one embodiment, the above problem is addressed by estimating the DOLP and AOLP associated with an over/underexposed pixel, from a prior distribution of degrees and angles that are known or partially known. In one example, the prior distribution may be based on smoothness assumptions where DOLP and AOLP are estimated from a neighboring quad block of pixels that are not over/underexposed. In another example, DOLP and AOLP may be estimated based on the geometry of an object through Fresnel equations. Once the degree and angle of polarization for the over/underexposed pixel are known, a corresponding exposure time may be estimated for the pixel. Thus, if there is at least one value in the quad block of pixels where the pixel is not over/underexposed, the pixel value may now be used for image irradiance reconstruction.

FIG. 2 is a conceptual layout diagram of a process for converting scene radiance into pixel values for the polarization camera 10 according to one embodiment. Incoming light associated with the scene is undergoes optical attenuation that varies depending on length of the path through the medium in which the light travels, to generate image irradiance I₀. The image irradiance is filtered by the polarization filter 16 which further changes the image irradiance based on the angle of polarization of the filter (e.g., by blocking light having angle of polarization that is different from the angle of polarization of the filter). In one embodiment, the polarization camera is configured to concurrently capture light at four different polarization angles, such as, for example, at 0°, 45°, 90°, and 135°, although some embodiments of the present disclosure are not limited thereto. In this regard, the image irradiance I₀ changes based on the polarization angle to generate a separate polarized irradiances for each angle. In the example where four polarization angles of 0°, 45°, 90°, and 135° are used, the corresponding polarization irradiances are I₁, I₂, I₃, I₄.

In one embodiment, the polarization irradiances pass through the color filter 17 which causes the polarization irradiances to further change according to a spectral response function of each of the color filters (e.g., where the color filters block or pass light of different wavelengths in accordance with their spectral response functions). Thus, after passing through the color filter, a separate polarized irradiance may be obtained for each of the color channels of the color filter, for each of the polarization angles. In the example where the color filter is an RGB color filter, each of the four polarization irradiances I₁, I₂, I₃, I₄ may further be modified into red, green, and blue polarized irradiances I_(1R), I_(1G), I_(1B), I_(2R), I_(2G), I_(2B), I_(3R), I_(3G), I_(3B), I_(4R), I_(4G), I_(4B).

In one embodiment, the color-filtered, polarized irradiances are captured by the image sensor 14, and digital images for each of the polarization angles 0°, 45°, 90°, and 135°, for each of the RGB color channels, are generated as follows:

L_(1R), L_(1G), L_(1B), L_(2R), L_(2G), L_(2B), L_(3R), L_(3G), L_(3B), L_(4R), L_(4G), L_(4B). In one embodiment, a response function 204 maps the image irradiance of an image pixel to the pixel values in the digital images for reconstructing the HDR image.

FIG. 3A is a flow diagram of a process executed by the processing circuit 100 for HDR image reconstruction according to one embodiment. It should be understood that the sequence of steps of the process is not fixed, but can be modified, changed in order, performed differently, performed sequentially, concurrently, or simultaneously, or altered into any desired sequence, as recognized by a person of skill in the art.

The process starts, and at block 300, the processing circuit 100 examines the pixel values of the polarized digital images L₁, L₂, L₃, L₄, and identifies, for each color channel, the over/underexposed pixels in the polar sense. In this regard, the processing circuit 100 examines each pixel value in a polarized digital image for each color channel, for determining whether the pixel value is above a first threshold or below a second threshold. If the pixel value is at or above the first threshold, the pixel value may be flagged as being overexposed. If the pixel value is at or below the second threshold, the pixel value may be flagged as being underexposed. In a typical 8-bit color image, the first threshold may be set to 255 (or substantially close to 255, e.g. 250), and the second threshold may be set to 0 (or substantially close to 0, e.g. 5).

In some cases, it is possible that a true value of a pixel is at a maximum or minimum value. Accordingly, in one embodiment, patch statistics is used for determining whether a pixel is over/underexposed. In this regard, a histogram of a spatial patch may be taken, and the distribution analyzed for estimating the likelihood that a pixel is over/underexposed.

In one embodiment, when two or more pixel values of a pixel are over/underexposed in two or more polarization angles for a particular color channel, the pixel may be flagged as being over/underexposed in the polar sense for the particular color channel.

At block 302, the processing circuit 100 selects a color channel with a fewest number of over/underexposed pixels in the polar sense. In one embodiment, the non-selected color channels are ignored and not used for image irradiance reconstruction. In this manner, the negative effect of over/underexposed pixels in the non-selected color channels may be minimized.

At block 304, the processing circuit 100 calculates a reconstructed image irradiance in the selected color channel. In one embodiment, the processing circuit estimates the image irradiance of each image pixel in the selected color channel, s_(C)(I₀), based on the pixel values of two or more pixels in the quad block of pixels obtained from the polarization images.

At block 306, the processing circuit 100 outputs a reconstructed HDR image in the selected color channel based on the reconstructed image irradiance values. In one embodiment, the output image has a dynamic range that is higher than the dynamic range supported by the image sensor 14.

FIG. 3B is a more detailed flow diagram of block 304 for reconstructing the image irradiance of pixels in an image in the selected color channel according to one embodiment. The process of FIG. 3B may be repeated for each image pixel in the selected color channel.

At block 310, a quad block of pixels in the selected color channel corresponding to the image pixel is evaluated to determine whether any of the pixels in the quad block are over/underexposed. In this regard, the corresponding pixel values in the polarization images may be examined to determine whether any examined pixel values are over a first threshold (hence, overexposed), or under a second threshold (hence, underexposed).

At block 312, a determination is made as to whether any of the pixels are over/underexposed. If the answer is NO, a weighted sum is calculated, at block 314, based on all the pixels in the quad block using the pixel values in each of the four polarization images according to the below formula 1:

${s_{C}\left( I_{0} \right)} = \left( {{\sum\limits_{i = 1}^{2}{{w\left( {L_{i,C} + L_{{i + 2},C}} \right)}{\left( {{g_{C}\left( L_{i,C} \right)} + {g_{C}\left( L_{{i + 2},C} \right)}} \right)/\left( {t_{0}{\sum\limits_{i = 1}^{2}{w\left( {L_{i,C} + L_{{i + 2},C}} \right)}}} \right)}}},{where}} \right.$ w(L) ∼ exp (−(L − 0.5)²/2σ²)

and σ is a standard deviation that is predefined for the formula. For example, σ=0.2 may be used as a default value.

Referring again to block 312, if there are any over/underexposed pixels in the quad block, a determination is made, at block 316, whether only one of the pixels is over/underexposed in the quad block, or whether there are more than one. If only one pixel is over/underexposed in the quad block, the processing circuit selects, at block 318, two pixels (L_(i,C) and L_(i+2,C)) that are not over/underexposed for estimating the image irradiance based on the two pixels. In one embodiment, the polarization images of the selected pixels are associated with polarization angles that are at 90 degrees from one another. In one embodiment, the image irradiance is calculated according to the below formula 2:

s _(C)(I₀)=½(g _(C)(L _(i,C))+g _(C)(L _(i+2,C)))

Referring again to block 316, if two or more of the pixels is over/underexposed in the quad block, then the image irradiance of the image pixel is calculated according to the above formula 1.

FIG. 4 is a conceptual layout diagram of images pixels and corresponding pixel values across different polarization images and color channels according to one embodiment. In the example of FIG. 4, polarized digital images 400-414 are generated for the various pixels 416, 418 of an image in different polarization angles (e.g. 0°, 45°, 90°, and 135°. Each of the polarization images contain different color channels such as, for example, the red, green, and blue color channels. In this regard, separate pixel values may exist for each color channel at each polarization angle. In the example of FIG. 4, a pixel value in a first polarization image in the red color channel 420, L_(1R), has a pixel value that is under/overexposed, while a pixel value in a second polarization image in the same red color channel 422, L_(2R), is within a range supported by the image sensor 14 and not under/overexposed.

In one embodiment, the processing circuit 100 examines the pixel values across the various polarization angles for each color channel, and determines whether a pixel should be flagged for the particular color channel. In the example of FIG. 4, the pixel values in the blue color channel for polarization images 400 and 404 in the blue color channel, L_(1B) and L_(3B), are either over or underexposed. Because there are at least two pixel values in the blue channel for a first image pixel 416 that are over or underexposed, the first image pixel 416 is flagged as being over/underexposed in the polar sense for the blue color channel. Similarly, because there are at least two pixel values in the red channel for a second image pixel 418 that are over or underexposed, the second image pixel 418 is flagged as being over/underexposed in the polar sense in the red color channel. Although pixel 428 in the fourth polarization angle for the blue color channel is also over/underexposed, the second image pixel 418 is not flagged as being over/underexposed in the polar sense in the blue color channel because the under/overexposure occurs in one polarization angle.

Smoothness Estimation of ρ and Θ

As discussed, a problem presented by over/underexposed pixels in a quad block is that they may prevent accurate estimation of the DOLP ρ and AOLP Θ. When four polarization angles are used in the quad block, three or four accurate pixel values are generally needed to estimate DOLP and AOLP using Stokes parameters. DOLP and AOLP further are needed to estimate camera exposure times, which in turn are needed for HDR image reconstruction according to current art algorithms.

As discussed in further detail in the above-referenced paper by X. Wu et al, “HDR Reconstruction Based on the Polarization Camera,” assuming four polarization angles at 0°, 45°, 90°, and 135°, the corresponding camera exposure times t₁, t₂, t₃, t₄ associated with each of the four polarization angles are calculated as follows:

$t_{1},{t_{3} = {\frac{t_{0}}{2}\left( {1 \pm {\rho\cos 2\theta}} \right){and}t_{2}}},{t_{4} = {\frac{t_{0}}{2}\left( {1 \pm {\rho\sin 2\theta}} \right)}}$

Once the camera exposure times are estimated, the image irradiance of an image pixel according to a current art HDR image reconstruction algorithm may be estimated from the quad block using pixel values across the four polarization angles according to the below equation:

${I_{0} = {{\frac{g\left( L_{i} \right)}{t_{i}}{for}i} = 1}},2,3,4$

In one embodiment, the computed image irradiance may be for a color channel with a fewest number of pixels that are over/underexposed in the polar sense. Accordingly, the embodiments described above for selecting such a color channel are also applicable to the current embodiment that estimates camera exposure times. In this regard, the computed image irradiance may be for the selected color channel based on the corresponding spectral function:

${{s_{C}\left( I_{0} \right)} = {{\frac{g_{C}\left( L_{i,C} \right)}{t_{i}}{for}i} = 1}},2,3,4$

The multiple image irradiance values I₀ or s_(C)(I₀) obtained per the above equations may then be combined (e.g. using a weighted sum) to obtain a final estimated irradiance value for a particular image pixel.

An embodiment of the present disclosure addresses the problem of over/underexposed pixels that may prevent estimation of the DOLP and AOLP, by estimating the DOLP and AOLP from a prior probability distribution of degrees and angles that are known or partially known. In one example, the prior distribution may be based on smoothness assumptions. For example, the DOLP and AOLP of a particular pixel having over/underexposed pixel values in the quad block, may be estimated using simple smoothing that interpolates DOLP and AOLP from a neighboring quad block (or multiple neighboring quad blocks) of pixels that are not over/underexposed, and that can therefore accurately measure DOLP and AOLP.

The smoothness assumption of DOLP and AOLP may involve a complex forward (i.e. rendering) model that takes into input the geometry and estimates of the refractive index and ambiguities of the object material. This may be referred to as the Stokes Rendering Block. In some embodiments, lighting must also be placed into the Stokes Rendering Block. The Stokes Rendering Block is a functional mapping that can therefore be implemented through a numerical model or a generative approach using encoder-decoder networks. In one embodiment, one such encoder-decoder network takes as input the coarse geometry and uses skip connections or normalization blocks that perform feature concatenation with the image. In one embodiment, these blocks help the decoder synthesize an unclipped DOLP and AOLP that are structurally high in frequency.

In another example, DOLP and AOLP may be estimated by assuming angular dominance, where DOLP and AOLP are assumed to be a function of the geometry of the object being imaged. In this regard, if the geometry of the object is known or partially known, DOLP and AOLP may be estimated through Fresnel equations. In one embodiment, the geometry of the object may be obtained from a prior known 3D model (e.g., a computer-aided design or CAD model or other vertex or point cloud model that defined in accordance with a plurality of 3D vertices or points) of the object that may be posed within a captured 3D reconstruction of the scene 1 and aligned with the polarization digital images. In some embodiments, stereo cameras may be integrated or used with the polarization camera 10 to obtain the object geometry. Once the degree and angle of polarization for a pixel is known, and if there is at least one value in one polarization angle in the quad block where the pixel is not over/underexposed, the pixel value may be used for image irradiance reconstruction.

FIG. 5 is a flow diagram of a process executed by the processing circuit 100 for HDR image reconstruction according to one embodiment. It should be understood that the sequence of steps of the process is not fixed, but can be modified, changed in order, performed differently, performed sequentially, concurrently, or simultaneously, or altered into any desired sequence, as recognized by a person of skill in the art.

At block 500, the processing circuit 100 examines a quad block of pixels of a given image pixel.

At block 502, a determination is made as to whether any over/underexposed pixels exist in the quad block. If the answer is NO, the processing circuit 100 calculates, at block 504, the DOLP and AOLP based on the pixel values in the quad block using the Stokes parameters. If, however, the answer is YES, the processing circuit 100 calculates, at block 506, the DOLP and AOLP from the neighboring pixels that accurately measure DOLP and AOLP, or using Fresnel equations that assume that DOLP and AOLP is a function of the geometry of the object being imaged.

Once DOLP and AOLP is computed, the processing circuit 100 computes, at block 508, the exposure times t₁, t₂, t₃, t₄ for respectively 0°, 45°, 90°, and 135° polarization angles for the quad block of pixels.

At block 510, the processing circuit 100 estimates a separate image irradiance I₀ based on each of the pixels in the quad block using the formula:

${I_{0} = {{\frac{g\left( L_{i} \right)}{t_{i}}{for}i} = 1}},2,3,4$

In one embodiment the estimated image irradiance may be for a selected color channel with a fewest number of over/underexposed pixels in the polar sense, s_(C)(I₀).

At block 512, the image irradiance I₀ may be estimated by combining the estimates for each of the separate pixels of the quad block as follows:

$I_{0} = \frac{\sum_{i = 1}^{4}{{W\left( L_{i} \right)}\left( {{g\left( L_{i} \right)}/t_{i}} \right)}}{\sum_{i = 1}^{4}{W\left( L_{i} \right)}}$

where W is a weight value that may depend on how well the pixels are exposed.

In the embodiment where s_(C)(I₀) is computed, the above equation may be modified to use the inverse response function g_(C) and pixel values L_(i,C) for the selected color channel.

In one embodiment, a weighted approach that is independent of the exposure times may also be used to combine the estimated image irradiance for each of the pixels in the quad block as follows:

$I_{0} = {\frac{\sum_{i = 1}^{2}{{W\left( {L_{i} + L_{i + 2}} \right)}{\left( {{g\left( L_{i} \right)} + {g\left( L_{i + 2} \right)}} \right)/t_{0}}}}{\sum_{i = 1}^{2}{W\left( {L_{i} + L_{i + 2}} \right)}}{or}}$ ${s_{C}\left( I_{0} \right)} = \left( {{\sum\limits_{i = 1}^{2}{{w\left( {L_{i,C} + L_{{i + 2},C}} \right)}{\left( {{g_{C}\left( L_{i,C} \right)} + {g_{C}\left( L_{{i + 2},C} \right)}} \right)/\left( {t_{0}{\sum\limits_{i = 1}^{2}{w\left( {L_{i,C} + L_{{i + 2},C}} \right)}}} \right)}}},} \right.$

At block 514, the processing circuit 100 outputs a reconstructed HDR image based on the reconstructed image irradiance. In one embodiment, the output image has a dynamic range that is higher than the dynamic range supported by the image sensor 14. In one exemplary use case, the reconstructed HDR image may be provided to a controller of a robotic arm for identifying and picking a correct object from a plurality of objects depicted in the reconstructed HDR image. The reconstructed HDR image may also be used by other machine vision or computer vision systems to detect objects robustly, such as, for example, machine or computer systems used in manufacturing, life sciences, self-driving vehicles, and the like.

According to one embodiment, HDR image reconstruction is implemented via an end-to-end neural network. The end-to-end neural network may be, for example, a neural decoder, encoder-decoder network, and or the like. In one embodiment, the end-to-end neural network is configured to take as an input, a plurality of polarization image features generated from the plurality of polarization images, and output a reconstructed HDR image having an expanded dynamic range. In one embodiment, the polarization image features may include the DOLP and AOLP values.

In one embodiment, the neural network may be trained based on training data. The training data may include a training set of polarization images corresponding to different angles of polarization and a corresponding training set of high dynamic range images. The training set of high dynamic range images may be captured using multiple exposures at different exposure settings. The training set of polarization images and the corresponding training set of high dynamic range images may be synthesized as described in PCT Application No. PCT/US21/12073, entitled “Systems and Method for Synthesizing Data for Training Statistical Models on Different Imaging Modalities Including Polarized Images,” the content of which is incorporated herein by reference.

According to various embodiments of the present disclosure, the processing circuit 100 is implemented using one or more electronic circuits configured to perform various operations as described in more detail below. Types of electronic circuits may include a central processing unit (CPU), a graphics processing unit (GPU), an artificial intelligence (AI) accelerator (e.g., a vector processor, which may include vector arithmetic logic units configured efficiently perform operations common to neural networks, such dot products and softmax), a field programmable gate array (FPGA), an application specific integrated circuit (ASIC), a digital signal processor (DSP), or the like. For example, in some circumstances, aspects of embodiments of the present disclosure are implemented in program instructions that are stored in a non-volatile computer readable memory where, when executed by the electronic circuit (e.g., a CPU, a GPU, an AI accelerator, or combinations thereof), perform the operations described herein to compute a segmentation map 20 from input polarization raw frames 18. The operations performed by the processing circuit 100 may be performed by a single electronic circuit (e.g., a single CPU, a single GPU, or the like) or may be allocated between multiple electronic circuits (e.g., multiple GPUs or a CPU in conjunction with a GPU). The multiple electronic circuits may be local to one another (e.g., located on a same die, located within a same package, or located within a same embedded device or computer system) and/or may be remote from one other (e.g., in communication over a network such as a local personal area network such as Bluetooth®, over a local area network such as a local wired and/or wireless network, and/or over wide area network such as the internet, such a case where some operations are performed locally and other operations are performed on a server hosted by a cloud computing service). One or more electronic circuits operating to implement the processing circuit 100 may be referred to herein as a computer or a computer system, which may include memory storing instructions that, when executed by the one or more electronic circuits, implement the systems and methods described herein.

While the present invention has been described in connection with certain exemplary embodiments, it is to be understood that the invention is not limited to the disclosed embodiments, but, on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims, and equivalents thereof. 

What is claimed is:
 1. A method for expanding a dynamic range associated with an image, the method comprising: capturing an image of a scene via an imaging device using a single exposure, the image of the scene comprising a plurality of polarization images corresponding to different angles of polarization, each of the polarization images comprising a plurality of color channels; determining a criterion for each of the plurality of color channels; selecting one color channel of the plurality of color channels based on determining of the criterion; generating a reconstructed image irradiance for the one color channel based on pixels in two or more of the plurality of polarization images obtained for the one color channel; and outputting a reconstructed image with the reconstructed image irradiance.
 2. The method of claim 1, wherein the reconstructed image irradiance in the one color channel has a higher dynamic range than irradiance supported by the imaging device.
 3. The method of claim 1, wherein the reconstructed image irradiance is based on a spectral irradiance associated with the one color channel.
 4. The method of claim 1, wherein the generating the reconstructed image irradiance for the one color channel includes: obtaining an inverse camera response function for the one color channel for mapping pixel values of the pixels to corresponding polarized irradiance values; and combining the polarized irradiance values.
 5. The method of claim 4, wherein the combining of the polarized irradiance values includes applying a weight to the polarized irradiance values.
 6. The method of claim 1, wherein the two of the polarization images are images captured at polarization angles that are 90 degrees apart.
 7. The method of claim 1, wherein the criterion is determining that the one color channel includes a most number of particular pixels, wherein each of the particular pixels are associated with pixel values in at least two of the plurality of polarization images, where the pixel values are above a first threshold or under a second threshold.
 8. The method of claim 1, wherein the generating the reconstructed image irradiance includes: identifying, for a particular pixel, a pixel value above a first threshold or under a second threshold; and in response to identifying the pixel value, estimating a degree of linear polarization (DOLP) and angle of linear polarization (AOLP) for the pixel based on a prior probability distribution of the DOLP and AOLP.
 9. The method of claim 8, wherein the prior probability distribution includes a DOLP and AOLP of one or more neighbor pixels to the particular pixel.
 10. The method of claim 8, wherein the prior probability distribution is formed based on known geometry of an object associated with the particular pixel.
 11. A method for expanding a dynamic range associated with an image, the method comprising: capturing an image of a scene via an imaging device using a single exposure, the image of the scene comprising a plurality of polarization images corresponding to different angles of polarization; identifying a pixel in one of the plurality of polarization images having a pixel value above a first threshold or under a second threshold; in response to identifying the pixel value, estimating a degree of linear polarization (DOLP) and angle of linear polarization (AOLP) for the pixel based on a prior probability distribution on the DOLP and AOLP; estimating a camera exposure time for each of the plurality of polarization angles based on the estimated DOLP and AOLP; generating a reconstructed image irradiance for the image based on pixel values in the plurality of polarization images and corresponding camera exposure times; and outputting a reconstructed image with the reconstructed image irradiance.
 12. The method of claim 11, wherein the reconstructed image irradiance has a higher dynamic range than irradiance supported by the imaging device.
 13. The method of claim 11, wherein the generating the reconstructed image irradiance includes: obtaining an inverse camera response function for mapping the pixel values to corresponding polarized irradiance values; and combining the polarized irradiance values.
 14. The method of claim 13, wherein the combining of the polarized irradiance values includes applying a weight to the polarized irradiance values.
 15. The method of claim 11, wherein the prior probability distribution includes a DOLP and AOLP of one or more neighbor pixels to the pixel.
 16. The method of claim 11, wherein the prior probability distribution is formed based on known geometry of an object associated with the pixel.
 17. A method for expanding a dynamic range associated with an image, the method comprising: capturing an image of a scene via an imaging device using a single exposure, the image of the scene comprising a plurality of polarization images corresponding to different angles of polarization, each of the polarization images comprising a plurality of color channels; generating a plurality of polarization image features based on the plurality of polarization images; and supplying the polarization image features to a convolutional neural network trained to generate a reconstructed image having an expanded dynamic range.
 18. The method of claim 17, wherein the generating the polarization image features comprises computing a degree of linear polarization (DOLP) and an angle of linear polarization (AOLP) based on the polarization images.
 19. The method of claim 17, wherein the convolutional neural network comprises a neural decoder.
 20. The method of claim 17, wherein the convolutional neural network comprises an encoder-decoder network.
 21. The method of claim 17, wherein the convolutional neural network is trained based on training data, wherein the training data includes a training set of polarization images corresponding to different angles of polarization and corresponding training set of high dynamic range images.
 22. The method of claim 21, wherein the training set of high dynamic range images are captured using multiple exposures at different exposure settings.
 23. The method of claim 21, wherein the training set of polarization images and the corresponding training set of high dynamic range images are synthesized.
 24. An imaging system comprising: a polarization camera comprising a polarizing filter configured to capture a plurality of polarization images using a single exposure, the plurality of polarization images corresponding to different angles of polarization, each of the polarization images comprising a plurality of color channels; and a processing system coupled to the polarization camera, the processing system comprising a processor and memory storing instructions that, when executed by the processor, cause the processor to perform: determining a criterion for each of the plurality of color channels; selecting one color channel of the plurality of color channels based on determining of the criterion; generating a reconstructed image irradiance for the one color channel based on pixels in two or more of the plurality of polarization images obtained for the one color channel; and outputting a reconstructed image with the reconstructed image irradiance.
 25. The system of claim 24, wherein the reconstructed image irradiance in the one color channel has a higher dynamic range than irradiance supported by the imaging device.
 26. The system of claim 24, wherein the reconstructed image irradiance is based on a spectral irradiance associated with the one color channel.
 27. The system of claim 24, wherein the generating the reconstructed image irradiance for the one color channel includes: obtaining an inverse camera response function for the one color channel for mapping pixel values of the pixels to corresponding polarized irradiance values; and combining the polarized irradiance values.
 28. The system of claim 27, wherein the combining of the polarized irradiance values includes applying a weight to the polarized irradiance values.
 29. The system of claim 24, wherein the two of the polarization images are images captured at polarization angles that are 90 degrees apart.
 30. The system of claim 24, wherein the criterion is determining that the one color channel includes a most number of particular pixels, wherein each of the particular pixels are associated with pixel values in at least two of the plurality of polarization images, where the pixel values are above a first threshold or under a second threshold.
 31. The system of claim 24, wherein the generating the reconstructed image irradiance includes: identifying, for a particular pixel, a pixel value above a first threshold or under a second threshold; and in response to identifying the pixel value, estimating a degree of linear polarization (DOLP) and angle of linear polarization (AOLP) for the pixel based on a prior probability distribution of the DOLP and AOLP.
 32. The system of claim 31, wherein the prior probability distribution includes a DOLP and AOLP of one or more neighbor pixels to the particular pixel.
 33. The system of claim 31, wherein the prior probability distribution is formed based on known geometry of an object associated with the particular pixel.
 34. An imaging system comprising: a polarization camera comprising a polarizing filter configured to capture a plurality of polarization images using a single exposure, the plurality of polarization images corresponding to different angles of polarization; and a processing system coupled to the polarization camera, the processing system comprising a processor and memory storing instructions that, when executed by the processor, cause the processor to perform: identifying, a pixel in one of the plurality of polarization images having a pixel value above a first threshold or under a second threshold; in response to identifying the pixel value, estimating a degree of linear polarization (DOLP) and angle of linear polarization (AOLP) for the pixel based on a prior probability distribution on the DOLP and AOLP; estimating a camera exposure time for each of the plurality of polarization angles based on the estimated DOLP and AOLP; generating a reconstructed image irradiance for the image based on pixel values in the plurality of polarization images and corresponding camera exposure times; and outputting a reconstructed image with the reconstructed image irradiance.
 35. The system of claim 34, wherein the reconstructed image irradiance has a higher dynamic range than irradiance supported by the imaging device.
 36. The system of claim 34, wherein the generating the reconstructed image irradiance includes: obtaining an inverse camera response function for mapping the pixel values to corresponding polarized irradiance values; and combining the polarized irradiance values.
 37. The system of claim 36, wherein the combining of the polarized irradiance values includes applying a weight to the polarized irradiance values.
 38. The system of claim 34, wherein the prior probability distribution includes a DOLP and AOLP of one or more neighbor pixels to the pixel.
 39. The system of claim 34, wherein the prior probability distribution is formed based on known geometry of an object associated with the pixel. 